Finite Group Databasebeta

← #26371336

Subgroups — #26371336

Order 12032.

612 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D376C211yesmaximal, characteristic, complemented
2#20245583C211yesmaximal, characteristic, complemented
3#20245566C211yesmaximal, characteristic, complemented
4#20245542C212yesmaximal, complemented
5#20245440C212yesmaximal, complemented
6#20245316C211yesmaximal, characteristic, complemented
7#20245299C211yesmaximal, characteristic
8#20245262C212yesmaximal, complemented
9#20245250C212yesmaximal, complemented
10#20245191C211yesmaximal, characteristic, complemented
11C47×#3168C211yesmaximal, characteristic, complemented
12C22×D376C2211yescharacteristic
13C2×C4×D188—21no—
14C2×#13093967C2212yes—
15C2×#13093965C2212yes—
16C4×D376—21no—
17C4×D376—21no—
18C4×D376C2212yes—
19C4×D376C2212yes—
20C2×#13093958C2211yescharacteristic
21C2×#13093946—21no—
22#15688950C2212yescomplemented
23#15688948C2212yescomplemented
24C4⋊(C47⋊C16)C2212yescomplemented
25#15688927C2212yescomplemented
26#15688924C2212yescomplemented
27#15688923C2212yes—
28#15688923C2212yes—
29C22⋊(C47⋊C16)C2211yescharacteristic
30C22⋊(C47⋊C16)C2211yescharacteristic
31#15688899C2212yescomplemented
32C47×#529—21no—
33C47×#499C2211yescharacteristic, complemented
34C47×#495C2211yescharacteristic, complemented
35C47×#488—21no—
36C47×#467C2211yescharacteristic
37C47×#466C2211yescharacteristic
38C47×#465—21no—
39C4×Q16×C47C2211yescharacteristic, complemented
40C4×SD16×C47—21no—
41C4×D8×C47C2211yescharacteristic, complemented
42C2×C4×C8×C47C2211yescharacteristic
43C22×D188—21no—
44C22×C4×D47—41no—
45C2×D376—21no—
46C2×D376—24no—
47C2×D376C2312yes—
48C4×D188—22no—
49C4×D188—22no—
50C4×D188—41no—
51C4×D188—41no—
52C2×C4⋊Dic47—21no—
53C2×(C2×D47)⋊C4—41no—
54#13093967—24no—
55#13093965—24no—
56C2×C47⋊C16C2312yes—
57C2×C47⋊C16C2312yes—
58#13093958—21no—
59#13093958C2312yes—
60#13093946—22no—
61#13093946—22no—
62C2×Q16×C47C2311yescharacteristic
63C2×SD16×C47—21no—
64C2×D8×C47C2311yescharacteristic
65C22×C8×C47D411yescharacteristic
66C22×C8×C47C2311yescharacteristic
67#126×C47—41no—
68#125×C47—21no—
69#124×C47—21no—
70#123×C47—41no—
71C22⋊Q8×C47—21no—
72#121×C47—21no—
73C4×Q8×C47—21no—
74C4×D4×C47—21no—
75C4×D4×C47—41no—
76#117×C47—41no—
77C2×C42×C47D411yescharacteristic
78#107×C47C2311yescharacteristic
79#107×C47C2311yescharacteristic
80#106×C47—21no—
81#103×C47—21no—
82#103×C47—21no—
83#102×C47—21no—
84#102×C47—21no—
85C4×C8×C47D411yescharacteristic
86C4×C8×C47D411yescharacteristic
87C4×C8×C47C2311yescharacteristic
88C4×C8×C47C2311yescharacteristic
89C23×D47—41no—
90C2×Q8×C47—21no—
91C2×D4×C47—21no—
92C2×D4×C47—41no—
93C22×C4×C47—41no—
94C22×C4×C47D811yescharacteristic
95C22×C4×C47D811yescharacteristic
96C22×C4×C47C2×D411yescharacteristic
97C22×Dic47—41no—
98C2×D188—24no—
99C2×D188—22no—
100C2×D188—42no—
101C2×D188—41no—
102C2×C4×D47—42no—
103C2×C4×D47—42no—
104C2×C4×D47—84no—
105Q16×C47—22no—
106SD16×C47—42no—
107D8×C47—22no—
108C2×C8×C47—22no—
109C2×C8×C47—41no—
110C2×C8×C47C2×D411yescharacteristic
111C2×C8×C47C2×D411yescharacteristic
112C2×C8×C47C2×D411yescharacteristic
113C2×C8×C47C2411yescharacteristic
114C4⋊C4×C47—21no—
115C4⋊C4×C47—21no—
116C4⋊C4×C47—41no—
117C4⋊C4×C47—41no—
118C4⋊C4×C47—41no—
119C4⋊C4×C47—41no—
120C22⋊C4×C47—41no—
121C22⋊C4×C47—41no—
122C22⋊C4×C47—41no—
123C22⋊C4×C47—41no—
124C22⋊C4×C47—41no—
125C42×C47—41no—
126C42×C47D811yescharacteristic
127C42×C47D811yescharacteristic
128C42×C47C2×D411yescharacteristic
129C42×C47C2×D411yescharacteristic
130(C2×D47)⋊C4—42no—
131(C2×D47)⋊C4—42no—
132C4⋊Dic47—22no—
133C4⋊Dic47—41no—
134D376—24no—
135D376—22no—
136D376#4114yes—
137C47⋊C16—22no—
138C47⋊C16—22no—
139C23×C47—41no—
140C23×C47C2×D811yescharacteristic
141C22×D47—44no—
142C22×D47—42no—
143C22×D47—82no—
144C22×D47—82no—
145Q8×C47—41no—
146Q8×C47—41no—
147D4×C47—41no—
148D4×C47—41no—
149D4×C47—82no—
150C2×C4×C47—22no—
151C2×C4×C47—21no—
152C2×C4×C47—21no—
153C2×C4×C47—41no—
154C2×C4×C47—41no—
155C2×C4×C47—41no—
156C2×C4×C47—41no—
157C2×C4×C47—82no—
158C2×C4×C47C2×D811yescharacteristic
159C2×C4×C47C2×D811yescharacteristic
160C2×C4×C47C2×D811yescharacteristic
161C2×C4×C47C2×D811yescharacteristic
162C2×C4×C47C2×D811yescharacteristic
163C2×C4×C47C22×D411yescharacteristic
164C2×Dic47—42no—
165C2×Dic47—82no—
166D188—24no—
167D188—44no—
168D188—42no—
169C4×D47—84no—
170C4×D47—84no—
171C8×C47—21no—
172C8×C47—21no—
173C8×C47—21no—
174C8×C47C2×#4112yes—
175#33674—471nomaximal, Sylow
176C22×C47—21no—
177C22×C47—21no—
178C22×C47—81no—
179C22×C47—81no—
180C22×C47—81no—
181C22×C47#50912yes—
182C22×C47C22×D811yescharacteristic
183C2×D47—44no—
184C2×D47—88no—
185C2×D47—82no—
186C2×D47—82no—
187C4×C47—21no—
188C4×C47—21no—
189C4×C47—21no—
190C4×C47—21no—
191C4×C47—21no—
192C4×C47—81no—
193C4×C47—81no—
194C4×C47—81no—
195C4×C47#52511yescharacteristic
196C4×C47#57511yescharacteristic
197Dic47—82no—
198#3168D4711yescharacteristic, complemented
199C2×C4×D8—471no—
200#2235—471no—
201#2232—471no—
202#2228—472no—
203#2210—472no—
204#2187—471no—
205#2184—471no—
206#2177—472no—
207#2175—472no—
208#2163—471no—
209C2×C47—22no—
210C2×C47—161no—
211C2×C47#310011yescharacteristic
212C2×C47C2×#50911yescharacteristic
213C2×C47#341411yescharacteristic
214D47—84no—
215C22×D8—471no—
216#529—21no—
217C2×C4×D4—941no—
218C2×SD32—472no—
219C2×D16—472no—
220#499C2×D4711yescharacteristic, complemented
221#495C2×D4711yescharacteristic, complemented
222#488—21no—
223#467C2×D4711yescharacteristic
224#466C2×D4711yescharacteristic
225#465—21no—
226C4×Q16C2×D4711yescharacteristic, complemented
227C4×SD16—21no—
228C4×D8—472no—
229C4×D8—472no—
230C4×D8—941no—
231C4×D8—941no—
232C4×D8C2×D4711yescharacteristic, complemented
233C2×#107—471no—
234C2×#102—941no—
235C2×C4×C8C2×D4711yescharacteristic
236#367—472no—
237#366—472no—
238C4⋊C16—472no—
239#358—472no—
240#357—472no—
241#357—472no—
242#357—472no—
243C22⋊C16—471no—
244C22⋊C16—471no—
245#346—472no—
246C47#3367411yescharacteristic, complemented, Sylow
247C22×D4—941no—
248C23×C4—1881no—
249C2×Q16C22×D4711yescharacteristic
250C2×SD16—21no—
251C2×D8—472no—
252C2×D8—944no—
253C2×D8—941no—
254C2×D8C22×D4711yescharacteristic
255C22×C8C22⋊D4711yescharacteristic
256C22×C8C22×D4711yescharacteristic
257#126—41no—
258#125—21no—
259#124—21no—
260#123—41no—
261C22⋊Q8—21no—
262#121—21no—
263C4×Q8—21no—
264C4×D4—21no—
265C4×D4—41no—
266C4×D4—942no—
267C4×D4—942no—
268C4×D4—1881no—
269C4×D4—1881no—
270#117—41no—
271C2×C4⋊C4—941no—
272C2×C22⋊C4—1881no—
273C2×C42C22⋊D4711yescharacteristic
274SD32—944no—
275D16—944no—
276C2×C16—472no—
277C2×C16—472no—
278#107—472no—
279#107—941no—
280#107C22×D4711yescharacteristic
281#107C22×D4711yescharacteristic
282#106—21no—
283#103—21no—
284#103—21no—
285#102—21no—
286#102—21no—
287#102—942no—
288#102—942no—
289C4×C8C22⋊D4711yescharacteristic
290C4×C8C22⋊D4711yescharacteristic
291C4×C8C22×D4711yescharacteristic
292C4×C8C22×D4711yescharacteristic
293C24—1881no—
294C2×Q8—21no—
295C2×D4—21no—
296C2×D4—41no—
297C2×D4—944no—
298C2×D4—942no—
299C2×D4—1882no—
300C2×D4—1881no—
301C22×C4—41no—
302C22×C4—3764no—
303C22×C4—1881no—
304C22×C4—1882no—
305C22×C4—1882no—
306C22×C4#1062533411yescharacteristic
307C22×C4#1062533411yescharacteristic
308C22×C4C2×C22⋊D4711yescharacteristic
309Q16—22no—
310SD16—42no—
311D8—22no—
312D8—474no—
313D8—944no—
314D8—942no—
315C2×C8—22no—
316C2×C8—41no—
317C2×C8C2×C22⋊D4711yescharacteristic
318C2×C8C2×C22⋊D4711yescharacteristic
319C2×C8C2×C22⋊D4711yescharacteristic
320C2×C8C23×D4711yescharacteristic
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—942no—
328C4⋊C4—1881no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—1882no—
335C22⋊C4—1882no—
336C42—41no—
337C42#1062533411yescharacteristic
338C42#1062533411yescharacteristic
339C42C2×C22⋊D4711yescharacteristic
340C42C2×C22⋊D4711yescharacteristic
341C16—942no—
342C16—942no—
343C23—41no—
344C23—3762no—
345C23—3762no—
346C23—1884no—
347C23—1882no—
348C23C2×#1062533411yescharacteristic
349Q8—41no—
350Q8—41no—
351D4—41no—
352D4—41no—
353D4—82no—
354D4—944no—
355D4—1884no—
356D4—1882no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—82no—
365C2×C4—3764no—
366C2×C4—3764no—
367C2×C4—3762no—
368C2×C4—1882no—
369C2×C4C2×#1062533411yescharacteristic
370C2×C4C2×#1062533411yescharacteristic
371C2×C4C2×#1062533411yescharacteristic
372C2×C4C2×#1062533411yescharacteristic
373C2×C4C2×#1062533411yescharacteristic
374C2×C4C22×C22⋊D4711yescharacteristic
375C8—21no—
376C8—21no—
377C8—21no—
378C8#41×D4712yes—
379C22—21no—
380C22—21no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—3768no—
385C22—3762no—
386C22—3762no—
387C22—1884no—
388C22#1568955812yes—
389C22C22×#1062533411yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—81no—
396C4—81no—
397C4—81no—
398C4—3762no—
399C4#1568963011yescharacteristic
400C4#1568992111yescharacteristic
401C2—22no—
402C2—161no—
403C2—3764no—
404C2#2025338411yescharacteristic
405C2C2×#1568955811yescharacteristic
406C2#2025652211yescharacteristic
subgroupG/H
centerC22C22×#10625334
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC47×#3168C2
socleC22×C47C22×D8
prime radical#20245299C2
hypercenter#3168D47
hypocenterC47#33674
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3168

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C4×D376C2semidirect
2. #20245583C2semidirect
3. #20245566C2semidirect
4. #20245542C2semidirect
5. #20245440C2semidirect
6. #20245316C2semidirect
8. #20245262C2semidirect
9. #20245250C2semidirect
10. #20245191C2semidirect
11. C47×#3168C2semidirect
22. #15688950C22semidirect
23. #15688948C22semidirect
24. C4⋊(C47⋊C16)C22semidirect
25. #15688927C22semidirect
26. #15688924C22semidirect
31. #15688899C22semidirect
33. C47×#499C22semidirect
34. C47×#495C22semidirect
39. C4×Q16×C47C22semidirect
41. C4×D8×C47C22semidirect
198. #3168D47semidirect
220. #499C2×D47semidirect
221. #495C2×D47semidirect
226. C4×Q16C2×D47semidirect
232. C4×D8C2×D47semidirect
246. C47#33674semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C4×D3762
#202455832
#202455662
#202455422
#202454402
#202453162
#202452992
#202452622
#202452502
#202451912
C47×#31682
#3367447